Lesson 5
Subtract Your Way
Warmup: Number Talk: Subtract a Little More (10 minutes)
Narrative
This Number Talk encourages students to think about subtraction with expressions that may require decomposing and to rely on using what they know about place value and counting up or back to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students subtract onedigit numbers from twodigit numbers.
When students notice that they can use the value of previously found expressions to find new values, they look for and make use of structure (MP7). This Number Talk provides opportunities for students to notice they can subtract to get to a ten, then subtract the rest (\(17  8 = 17  7  1 = 10  1 = 9\)).
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(17  7\)
 \(17  8\)
 \(26  6\)
 \(26  8\)
Student Response
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Activity Synthesis
 “How could you use the third expression to help you find the difference of the last expression?” (I know that taking away 6 gets me to 20, then I just took 2 more away.)
Activity 1: How Do You Find the Value? (20 minutes)
Narrative
The purpose of this activity is for students to subtract in a way that makes sense to them. Students use a method of their choice and share their methods with one another. This can serve as a formative assessment of how students approach finding the value of a difference when a ten must be decomposed when subtracting by place. Although students may use many methods to subtract, including those based on counting or compensation, the synthesis focuses on connecting these methods to those based on place value where a ten is decomposed.
Monitor and select students with the following methods to share in the synthesis:
 Uses connecting cubes to make 82 and removes 9 blocks. Counts back or counts all to find the difference.
 Subtracts 2 from 82 to get to a ten, 80, and then subtracts 7 from 80 by counting back (with or without blocks).
 Uses baseten blocks to show 82 and decomposes a ten to get 12 ones. Subtracts 9 ones from 12 ones and counts the remaining blocks.
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to connecting cubes and baseten blocks.
Activity
 “Find the difference for \(82  9\).”
 “Show your thinking using drawings, numbers, or words.”
 “Be prepared to share your thinking.”
 As student work, consider asking:
 “What did you do first? Why?”
 “What did you take away first? Why?”
 “How did you show 82 at first? Did you have to make any changes to take away 9? Explain.”
 “What tool did you use? Why?”
Student Facing
Find the value of \(82  9\).
Show your thinking. Use blocks if it helps.
Student Response
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Activity Synthesis
 Ask selected students to share in the given order.
 “Why did _____ need to change 82 to 7 tens and 12 ones to subtract ones from ones?” (There are too many ones to take away, so she traded a ten for 10 ones to show decomposing a ten.)
Activity 2: Subtract with Baseten Blocks (15 minutes)
Narrative
The purpose of this activity is for students to subtract a onedigit number from a twodigit number. In the previous activity, students shared many ways to subtract including using connecting cubes or baseten blocks to show decomposing a ten. They build on this understanding as they use baseten blocks to represent the starting number and subtract an amount that requires them to decompose a ten.
Advances: Speaking, Conversing
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give each group access to baseten blocks.
Activity
 “Diego was representing numbers using baseten blocks. Work with a partner to follow along and see what Diego discovered.”
 “Use your blocks first to show what Diego does. Then answer any questions.”
 8 minutes: partner work time
 Monitor for students who talk about “exchanging” or “trading” a ten for ten ones.
Student Facing

Diego started with 5 tens and 5 ones. Represent Diego’s blocks with the baseten blocks.
How many does he have?

Diego took away 2 tens.
 Draw a representation to show what happened to Diego’s blocks.
 Write an equation to show how many Diego has now.

Then, Diego took away 8 ones.
 Draw a diagram to show what happened to Diego’s blocks.
 Write an equation to show how many Diego has now. Be prepared to explain your reasoning.
Student Response
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Advancing Student Thinking
Some students may get the ones they need, but also keep the ten. Consider asking:
 “Why did you add 10 ones to Diego’s blocks?”
 “What is the value of the blocks now?”
 “When you decompose a tower of ten, what happens to the tower? How could you show this with the baseten blocks?”
Activity Synthesis
 “What did you need to do with the blocks when Diego took away 8 ones?”
 Select previously identified students to share.
 “What is different about using baseten blocks compared to the towers of ten?” (With the towers we could break it apart, but with the baseten blocks we had to give a ten and take out 10 ones.)
 “When you subtract by place, sometimes you need to decompose a ten to subtract ones. When we use connecting cubes, we can show those by breaking apart or decomposing a tower of ten.”
 “When we use baseten blocks, we can't break apart the ten into ones, but we can still show decomposing it by replacing 1 ten with 10 ones.”
Lesson Synthesis
Lesson Synthesis
“In this lesson, we learned that we can decompose a ten into 10 ones to subtract. We used towers of ten and baseten blocks and drew baseten diagrams to represent decomposing a ten.”
Write \(35  8\).
Display 35 using blocks as 3 tens and 5 ones and 2 tens and 15 ones.
\(35 = 20 + 15\)
“How could representing 35 the second way help us find the difference?” (We have enough ones to take away 8.)
Cooldown: Find the Difference (5 minutes)
CoolDown
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